Mathematical Conditions for Induced Cell Differentiation and Trans-differentiation in Adult Cells

We present a theoretical framework for the analysis of the effect of a fully differentiated cell population on a neighboring stem cell population in Multi-Cellular Organisms (MCOs). Such an organism is constituted by a set of different cell populations, each set of which converges to a different cycle from all possible options, of the same Boolean network. Cells communicate via a subset of the nodes called signals. We show that generic dynamic properties of cycles and nodes in random Boolean networks can induce cell differentiation. Specifically we propose algorithms, conditions and methods to examine if a set of signaling nodes enabling these conversions can be found. Surprisingly we find that robust conversions can be obtained even with a very small number of signals. The proposed conversions can occur in multiple spatial organizations and can be used as a model for regeneration in MCOs, where an islet of cells of one type (representing stem cells) is surrounded by cells of another type (representing differentiated cells). The cells at the outer layer of the islet function like progenitor cells (i.e. dividing asymmetrically and differentiating). To the best of our knowledge, this is the first work showing a tissue-like regeneration in MCO simulations based on random Boolean networks. We show that the probability to obtain a conversion decreases with the log of the node number in the network, showing that the model is relevant for large networks as well. We have further checked that the conversions are not trivial, i.e. conversions do not occur due to irregular structures of the Boolean network, and the converting cycle undergoes a respectable change in its behavior. Finally we show that the model can also be applied to a realistic genetic regulatory network, showing that the basic mathematical insight from regular networks holds in more complex experiment-based networks.